This is an interface to the Cumulative Distribution Function package present in the GNU Scientific Library.

Let us have a continuous random number distributions are defined by a probability density function p(x).

The cumulative distribution function for the lower tail P(x) is defined by the integral of p(x),
and gives the probability of a variate taking a value less than x.
These functions are named cdf_NNNNNNN_P().

The cumulative distribution function for the upper tail Q(x) is defined by the integral of p(x),
and gives the probability of a variate taking a value greater than x.
These functions are named cdf_NNNNNNN_Q().

The inverse cumulative distributions,
x = Pinv(P) and x = Qinv(Q) give the values of x which correspond to a specific value of P or Q.
They can be used to find confidence limits from probability values.
These functions are named cdf_NNNNNNN_Pinv() and cdf_NNNNNNN_Qinv().

For discrete distributions the probability of sampling the integer value k is given by p(k),
where sum_k p(k) = 1.
The cumulative distribution for the lower tail P(k) of a discrete distribution is defined as,
where the sum is over the allowed range of the distribution less than or equal to k.

The cumulative distribution for the upper tail of a discrete distribution Q(k) is defined as giving the sum of probabilities for all values greater than k.
These two definitions satisfy the identity P(k) + Q(k) = 1.